Let's solve each equation step by step.

a) $2z - 5 - 5z = 7 + 3z - 3$

1. Combine like terms on both sides: $(2z - 5z) - 5 = (3z + 7 - 3)$ $-3z - 5 = 3z + 4$

2. Move all terms involving $z$ to one side: $-3z - 3z = 4 + 5$ $-6z = 9$

3. Solve for $z$: $z = \frac{9}{-6} = -\frac{3}{2}$

Thus, $z = -\frac{3}{2}$.

b) $3 \left( x + \frac{1}{5} \right) = \frac{1}{2}x - 7$

1. Distribute the 3 on the left-hand side: $3x + \frac{3}{5} = \frac{1}{2}x - 7$

2. Multiply through by 10 (to eliminate fractions): $10 \left( 3x + \frac{3}{5} \right) = 10 \left( \frac{1}{2}x - 7 \right)$ $30x + 6 = 5x - 70$

3. Move the $x$-terms to one side: $30x - 5x = -70 - 6$ $25x = -76$

4. Solve for $x$: $x = \frac{-76}{25}$

Thus, $x = \frac{-76}{25}$.

c) $3(2 - m) = 5m$

1. Distribute the 3: $6 - 3m = 5m$

2. Move all $m$-terms to one side: $6 = 5m + 3m$ $6 = 8m$

3. Solve for $m$: $m = \frac{6}{8} = \frac{3}{4}$

Thus, $m = \frac{3}{4}$.

d) $0.05(t + 3) = -0.09 + 0.13t - 4$

1. Distribute the $0.05$ on the left-hand side: $0.05t + 0.15 = -0.09 + 0.13t - 4$

2. Combine constants on the right-hand side: $0.05t + 0.15 = 0.13t - 4.09$

3. Move all $t$-terms to one side: $0.05t - 0.13t = -4.09 - 0.15$ $-0.08t = -4.24$

4. Solve for $t$: $t = \frac{-4.24}{-0.08} = 53$

Thus, $t = 53$.

Would you like any further details on any of the steps? Here are 5 related questions:

1. How do you handle equations with variables on both sides?
2. What is the best method to simplify fractions during equation solving?
3. How can you verify your solutions to these types of equations?
4. What are strategies for solving equations with decimals?
5. What are common mistakes to avoid when solving linear equations?

Tip: When dealing with fractions, it can be helpful to multiply through by the least common denominator to eliminate them early on.